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Journal of Global Optimization

, Volume 34, Issue 3, pp 427–440 | Cite as

Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

  • S. J. LiEmail author
  • K. L. Teo
  • X. Q. Yang
  • S. Y. Wu
Article

Abstract

This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established.

Keywords

generalized vector quasi-equilibrium problem nonlinear scalarization function minimax inequality 

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References

  1. 1.
    Ansari, Q.H., Fabian, , Flores-Bazan,  2003Generalized vector quasi-equilibrium problems with applicationsJournal of Mathematical Analysis and Applications277246256CrossRefGoogle Scholar
  2. 2.
    Aubin, J.P., Ekeland, I. 1984Applied Nonlinear AnalysisJohn Wiley and SonsNew YorkGoogle Scholar
  3. 3.
    Chen, G.Y., Goh, C.J., Yang, X.Q. 1999Vector network equilibrium problems and nonlinear scalarization methodsMathematical Methods of Operation Research49239253Google Scholar
  4. 4.
    Chen, G.Y., Goh, C.J., Yang, X.Q. 2000On gap functions for vector variational inequalitiesGiannessi, F. eds. Vector Variational Inequalities and Vector EquilibriaKluwer Academic PublishersDordrecht, Holland5572Google Scholar
  5. 5.
    Chen, G.Y., Yang, X.Q. and Yu, H. (2004), A nonlinear scalarization function and generalized quasi-vector equilibrium problems, Journal of Global Optimization. In press, available online.Google Scholar
  6. 6.
    Gerth, C., Weidner, P. 1990Nonconvex separation theorems and some applications in vector optimizationJournal of Optimization Theory and Applications67297320CrossRefGoogle Scholar
  7. 7.
    Ha, C.W. 1980Minimax and fixed point theoremsMathematische Annalen2487377CrossRefGoogle Scholar
  8. 8.
    Konnov, I.V., Yao, J.C. 1999Existence of solutions for generalized vector equilibrium problemsJournal of Mathematical Analysis and Applications233328335CrossRefGoogle Scholar
  9. 9.
    Kuroiwa, D. 1996Convexity for set-valued mapsApplied Mathematics Letter997101Google Scholar
  10. 10.
    Li, S.J., Teo, K.L., Yang, X.Q. 2005Generalized vector quasi-equilibrium problemsMathematical Methods of Operations Research613Google Scholar
  11. 11.
    Li, S.J., Teo, K.L. and Yang, X.Q., On generalized vector quasi-equilibrium problems,preprint.Google Scholar
  12. 12.
    Li, S.J., Yan, H., Chen, G.Y. 2003Differential and sensitivity properties of gap functions for vector variational inequalitiesMathematical Methods of Operations Research57377391Google Scholar
  13. 13.
    Yang, X.Q. 2003On the gap functions of prevariational inequalitiesJournal of Optimization Theory and Applications116437452CrossRefGoogle Scholar
  14. 14.
    Yang, X.Q., Yao, J.C. 2002Gap functions and existence of solutions to set-valued vector variational inequalitiesJournal of Optimization Theory and Applications115407417CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • S. J. Li
    • 1
    Email author
  • K. L. Teo
    • 2
  • X. Q. Yang
    • 3
  • S. Y. Wu
    • 4
    • 5
  1. 1.Department of Information and Computer Sciences, College of Mathematics and ScienceChongqing UniversityChongqingChina
  2. 2.Department of Mathematics and StatisticsCurtin University of TechnologyPerthAustralia
  3. 3.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityKowloonHong Kong
  4. 4.Institute of Applied MathematicsNational Cheng-Kung UniversityTainanTaiwan
  5. 5.National Center for Theoretical SciencesTaiwan

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